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Solar nergyVol . 47, No. 1 , p . 49-55 , 1991 0038-092X/91 3.00 + .60

Printed in the U,S.A. Copyright 1991 Perga mo n Press plc

S O L R R D I T I O N C H R C T E R I S T IC S I N B U D H B I

ALl M. EL-NASHAR

Water and Electricity Department, Abud Dhabi, United Arab Emirates

Abstract--Based on the instantaneous global and diffuseradiation measurements made in Abu Dhabi, UAE,

during 1987, the instantaneous values of the clearness index, diffuse fraction, atmospheric transmittance,

and extinction coefficientwere estimated and found to be strongly dependent on the air mass and month

of the year. Therefore, correlations between each of these parameters versus the air mass and month of the

year were developed using the least-squares echnique. The diffuse fraction may alternatively be correlated

against he dearness index and the air mass with no seasonal nfluence.The beam transmittance was estimated

theoretically using the two-layer atmospheric model and making use of the correlation developed previously

for the extinction coefficient. The model was found to yield satisfactory results. The diffuse transmittance

was also estimated theoretically using both the RSC model and the isotropic scattering model with good

agreement with the data obtained.

1 . M E A S U R E M E N T

Both the global and diffuse radiations were measured

at the Solar Desalination Plant in Abu Dhabi, UAE

(lati tude 24.5 ON, longitude 54.3 E), using three pyra-

nometers. The global measure ments were taken using

two pyranometers while the third pyr anometer had a

shadow band installed in order to enable the diffuse

component to be measured. One of the global mea-

surements was taken continuously using one pyra-

nometer (manufactured by Nakaasa Instrument Co.

of Japan, Model H-201 ) which was tilted at an angle

equal to the incl inat ion of the collector absorber plate

(20 due sout h). This inst rumen t was connected di-

rectly to the data acquisition system (DAS) which

consists ofa Thermodac 32 machine manufactured by

Eto Denki Co. of Japan. The DAS receives continu-

ously all the measurement signals from the plant for

subsequent processing. This pyranometer was cali-

brated just before the commencement of testing. In

the DAS, the global solar radiation measurement was

integrated over one-h our intervals to yield the ho urly

values of global solar radiation on the tilted surface.

The same measurement was also routed to a chart re-

corder which continuousl y plots the instantaneous

global solar radiation versus time. These global solar

radiation measurements were converted to corre-

sponding values on a hor izonta l surface using standard

methods [ 1 .

The second measurement of global radiation was

taken by a similar pyranometer located on a horizontal

surface with the measurements taken m anuall y once

every hour du ring daytime. The diffuse compon ent on

a horiz ontal surface was obtai ned by an identical pyra-

nometer with a shadow band attached to it to prevent

beam radiation from reaching the glass dome of the

pyranometer. Measurement of the diffuse componen t

was also taken ma nua lly every hour. Two digital volt-

meters were used to measure the hourly global and

diffuse radiation. The two pyranome ters used for mak-

ing these m anua l measurements were calibrated against

the one directly connected to the d ata acqui sition sys-

tem by first adjusting the tilt angle of the later pyra-

nometer to make it horizontal and removing the

shadow band, then comparing the instant aneous mea-

surement values of the three pyranometers.

2 . D A T A A N A L Y S I S

The weather in A bu Dhabi is extremely sunny and

dry with the annual precipitation rarely exceeding 50

ram. The skies are mostly clear during most of the

winter months, and only during few days in January

and February that overcast skies are observed. Dur ing

the sum mer months , however, days with hazy weather

are encountered. In these days, the air will be laden

with fine sand particles that usually precipitate on

ground objects.

With this in mind, most of the data presented in

this paper are for clear skies without any cloud cover.

Days with hazy weather are also included in the clear

sky data.

2 1 T he dear nes s i ndex

The clearness index is defined as the ratio of the

inst anta neous global radiat ion on a hor izontal surface

on the ground to the corresponding quantity outside

the earth s atmosphere. The extraterrestrial solar ra-

diat ion on a horizo ntal surface was estimated from the

radiat ion on a normal surface and the solar altitude at

a particular time.

Data for the clearness index based on mea sure ment

of solar radiation taken o n clear days duri ng 1987 are

plotted against the air mass in Fig. 1. The data exhibit

substantial scatter which suggests that there are other

factors affecting the clearness index in additi on to the

air mass. The c umulat ive effects of those factors results

in changes in the compositi on of the air through which

radia tion is going through. A least-square fit of the data

in this figure results in a correlation of the form

kt = 0.75 exp (- 0.0 933 m) ( 1 )

The clearness index varies during the day reaching its

lowest value soon after sunrise and just before sunset

49

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50

x ~

g

E

o

L o c a t io n : A b u D h a b i . 2 4 . 5 N , 5 4 . 3 E

~ a r : 1 9 8 7

1 . 0

. 8

,6

. 2 -

0 c

k : 0 . 7 5 e ( ' 0 ' 0 9 3 3 r n )

t

, . . ~ , . . ,

~ 1 . . - . . .

i l

A i r m a s s . m

Fig. 1. Clearness index vs. air mass 1987).

and attains its highest value near noon. In addition to

its diurn al variation , the clearness index has also a sea-

sonal variation. The clearness index data were sorted

out according to the air mass and the month of the

year, and the data were then fitted to second degree

polyn omia ls using the least-squares technique. Figure

2 shows the variation of the clearness index with the

air mass for different months for 1987. The clearness

index can be seen to reach its lowest values during

July, whereas in January its highest values are attained.

These results are a testimony of the variation in the

condition of the air between the summer and winter

months. During summer mon ths e.g., Jul y), the level

of fine dust particles in the air as well as the relative

humidity are higher than that during winter months

e.g., January). This situation can be expected to cause

an additional attenuating effect on the solar radiation

penetrating the atmosphere in the summer months,

thus resulting in a lower clearness index dur ing those

months.

A. M. EL-NASHAR

months are shown in Fig. 4. For a particular day, the

diffuse fraction can be seen to att ain its mi nimu m value

near noo n time i.e., at lowest air mass), and increases

gradually as the air mass increases. It can also be seen

tha t there is a strong seasonal effect on the diffuse frac-

tion with this fraction being higher in summer t han in

winter.

It is customary to express the diffuse fraction in

terms of the clearness index. Several investigators have

developed correlations between the diffuse fraction and

the clearness index starting with the early work of

Page[2] and of Liu and Jor dan[ 3]. The effect of the

air mass on the shape of such correlations was, however,

absent in most of them. By sorting the data on the

diffuse fraction according to the value of the clearness

index, the air mass, and the month of the year, it was

possible to identify the effect of each of these three

variables on the diffuse fraction.

The d versus k , data for constant air mass and for

a particular month o f the year were fitted to exponent ial

curves using the least-squares method. The exponentia l

curves have the form

d k t, m ) = e x p - a k t ) b + c m ) 2)

where a, b, and c are constants. Typical results using

the data for 1987 are shown in Figs. 5 and 6. In these

figures the diffuse fraction is plotted against the clear-

ness index for different air mass ranges.

2.3 T h e a t m o s p h e r i c t r a n s m i t t a n c e

The atmos pheric tra nsmit tance is defined as the ra-

tio of beam radiation on a horizontal surface to the

extraterrestrial radiation on a horizontal surface when

the sun is at the zenith. For any solar altitude, the

atmospheric transmit tance may be calculated from the

relation

2.2

T h e d i f f u s e f r a c t i o n

The diffuse fraction is defined as the ratio between

the instantaneous diffuse radiation falling on a hori-

zontal surface and the global radiation falling on the

same surface. This ratio has both d iurn al and seasonal

variations. Durin g a particu lar clear day, it reaches its

highest value soon after sunrise and jus t before sunset,

with the trend being opposite to that of the clearness

index.

The data for the diffuse fraction for clear days dur ing

1987 are plotted against the air mass in Fig. 3. As can

be seen, there is a considerable scatter in the da ta bu t

the trend is obvious, namely, the diffuse fraction is

lowest at noon time mi ni mu m m), and increases as

the air mass increase. A linea r least-squares fit of this

data gives a correlation of the form:

d = 0.123 + 0.0894m.

The collected data on the diffuse fraction were also

sorted out according to the air mass and the mon th o f

the year, an d were fitted to polynomials of the second

degree. The resulting correlations for the different

Gbl ]/m)

where P is the atmospheric transmittance Gb is the

instantaneous beam radiat io n on a h or izon ta l surface

1 00

0 . 8 0

O . 6 0

~ O . 4 0

G

0 . 2 0

. . .. ~ ~ . . ~ . . . . ~ ~ .

1 2 3 4 5

m

o i r m Q s s

JAN

NOV

Fig. 2. Clearness ndex vs. air mass for January, March, May,

July, September, and November 1987.

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Solar radiation characteristics in Abu Dhabi

Loca tion : Abu Dhabi, 24.5 N, 54,3E

T yea r : 1987

- -

d = 0 ~ 2 3 , 0 0 8 9 3 6 m

s ~

\. .

2 4 ' , . ' : . . . .

e~ , . l l :~ '~ ' ' ' ' : '

2 . : '

~ 2 J Z

s ~ ~ 8 9 l b

A i r m a s s , m

Fig. 3. Diffuse fraction vs. air mass 1987).

1.0

o

.6-

.4 -

Location: A I~ Dhobi, 24.5N, 5 / . 3 E

year: 1987

m = [ 1 4 - 1 6 )

.2-

,

, . . - - d : 1 0 9 8 5 e i 2 5 6 k t )

51

Clearness index

Fig. 5. Diffuse fraction vs. clearness index 1987).

and G o is the in stan tane ous extraterrestrial radiation

on a horizontal surface. It can be seen that at the zenith,

m = l, the atmospheric transmitta nce conform to the

defini tion stated above.

The atmospheric transmittance represents the ex-

tent which the atmosphere allow the solar radiat ion to

penetrate through it without being absorbed or scat-

tered. It may be related to the familiar extinctio n coef-

ficient by wr iting the following equalities

G b = G a r . e x p - O g n L )

= G o P m

4 )

where r. = transmittance of the upper layer of the

a t m o s p h e r e ; B e = the extinction coefficient; and L

= length of the bottom layer of the atmosphere. We

can therefore express the atmospheric transmittance

a s

p - rxl l/m)

= [ r,exp -- hf+,rnz+) . 5)

The value of P varies during the day and also has a

distinct seasonal variation. Figure 7 shows this daily

and seasonal variat ion for two typical days in Janua ry

and June. In this figure the transmittance is plotted

versus the h our o f the day. It can be seen that for any

day the transm ittance is highest early in the mor ning

and late in the aft ernoon, an d reaches its lowest value

1 . 0 0

- I~ 0 .80

g 0 . 6 0

+d

g

0 4 0

~ 0 . 2 0

0 O0

_

~. . . .

, . . . /

2 4

m

a i r m u s s

Jl~.v

JAN

Fig. 4. Diffusefraction vs. air mass for January, March, May,

July, September, and November 1987).

near noon time. Moreover, the transmittance during

January and generally during all winter months) is

substantially higher than that duri ng June and all the

other summer mont hs). This may be attributed to the

heavy dust con tent in the air as well as the high relative

humidi ty experienced during the summe r mont hs as

compared to winter months.

The transmittance of the upper layer may be esti-

mated from a plot of the beam fraction against the air

mass. The beam transm ittance may be obtained from

the clearness index an d diffuse fraction using the def-

initio n of the beam transmittance

b

kb = - 6)

G o

= 1 - d ) k t 7)

Typical values for kb are plotted against the air mass

m in Fig. 8. The tr end appears to be linear in the range

of air mass used. The transmittance of the upper at-

mospheric layer may be obtained by extending the

straight line to m = 0; this gives r, = 0.75. Based on

this value, the extinction coefficient of the lower at-

mospheric layer may be expressed in terms of the

x~

.8

.6

=~ .~-

c3

. 2 -

Location: Ab u Dhabi, 24. 5*N , 54.30E

year : 1987

m = ( 2 5 - 3 . 5 )

~ -- d : 1 2 5 6 e q 8 9 2 k t )

C~eomess inde x, k

Fig. 6. Diffuse fraction vs. clearness index 1987).

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52 A .M . EL-NASHAR

atmospheric trenumltlafloe P

1

0 . 8 ~ :

Table 1. V alues of the constants a a nd b for each

month of 1987

M onth Value of constant a Value of constant b

o . e ~ - ; i ~ - ~ - ~ Janu ary

o.( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Feb ruary

March

o =

A pr i l

M a y

13 i i i I i i t i

: 3 0 8 : 0 9 . 3 0 1 0 : 3 0 1 1 :3 0 1 2 : 3 0 1 3 : 3 0 1 4 =3 0 1 & 3 0 1 6 : 3 0 1 7 : 3 0 June

t ime of day uly

August

- - J a n u a r y 1 9 8 7 - 4 - - J u n e 1 9 8 7 September

Fig. 7. Atmospher ic t ransmittance at Abu Dhabi ( la t i tude Octob er

24.5N, longitude 54.3E) . Nov emb er

December

0.66 0.013

0.65 0.018

0.57 0.026

0.61 0.014

0.54 0.027

0.47 0.006

0.45 0.006

0.54 0.010

0.56 0.010

0.59 0.020

0.59 0.030

0.65 0.010

a t m o s p h e r i c t r a n s m i t t a n c e P a n d t h e a i r m a s s m a s

f o l l o w s :

/~ e= _ [ 0 ~ 9 + I n ( P ) ] .

( 8 )

S i m i l a r t o t h e a t m o s p h e r i c t r a n s m i t t a n c e , t h e e x t i n c -

t i o n c o e f f i c ie n t w a s a l s o f o u n d t o b e i n f l u e n c e d b y t h e

a i r m a s s a n d t h e s e a s o n o f t h e y e a r . F o r a p a r t i c u l a r

d a y , t h e e x t i n c t i o n c o e f fi c i en t i s la r g e s t n e a r n o o n t i m e

( l o w e s t a i r m a s s ) a n d t h e n d r o p s d o w n a s w e m o v e

a w a y f r o m n o o n t i m e . T h i s t r e n d i s sh o w n c l e a rl y i n

F i g . 8 w h i c h g i v e s tw o p l o t s o f fie v e r s u s m o b t a i n e d

f r o m l e a s t -s q u a r e s f it o f e x p e r i m e n t a l d a t a o b t a i n e d

f o r J a n u a r y a n d J u n e 1 98 7. O n e c a n o b s e r v e fr o m t h e s e

f i g u r es t h a t t h e e x t i n c t i o n c o e f f i c i e n t i s a s t r o n g f u n c -

t i o n o f t h e s e a s o n o f t h e y e a r . T h i s a g a i n r e f le c t s t h e

s e a so n a l v a r i a t io n i n t h e c o n d i t i o n o f t h e a t m o s p h e r e

a s i n fl u e n c e d b y i t s c o n t e n t o f d u s t a n d w a t e r v a p o r

( h u m i d i t y ) , a n d p o s s i b ly o t h e r c o n s ti t u en t s .

F o r a n y p a r t i c u l a r d a y , t h e a t m o s p h e r i c t r a n s m i t -

t a n c e w a s f o u n d t o d e p e n d o n t h e a i r m a s s a n d t h e

m o n t h o f t h e y e a r. T h e r e l a ti o n s h i p b e t w e e n t h e a t -

m o s p h e r i c t r a n s m i t t a n c e a n d t h e a i r m a s s i s a p p r o x i -

m a t e l y l i n e a r a n d t h e e x p e r i m e n t a l d a t a w e r e t h e r e fo r e

f i tt e d t o a s tr a i g h t l i n e o f t h e f o r m P ( m ) = a + b . m ,

w h e r e t h e c o n s t a n t s a a n d b a r e d e p e n d e n t o n t h e

m o n t h o f t h e y e a r. T h e v a l u e o f t h e se c o n s t a n t s w h i c h

w e r e o b t a i n e d f o r A b u D h a b i u s i n g th e 1 98 7 d a t a a n d

a r e g i v e n i n T a b l e 1 .

W i t h t h e a t m o s p h e r i c t r a n s m i t t a n c e k n o w n , i t i s

n o w p o s s i b l e to e s t i m a t e t h e e x t i n c t i o n c o e f fi c ie n t /3 8

a s a f u n c t i o n o f th e a i r m a s s m a n d t h e m o n t h o f t h e

y e a r . S u b s t i t u t i n g t h i s l i n e a r re l a t i o n s h i p f o r P ( m ) i n

e q n ( 8 ) y i e l d s

B e ( m , i ) = - [ 0 ~ 9 + l n ( a + b m ) 1 .

T h e e x t i n c t i o n c o e f fi c i en t is s e e n t o h a v e a s t r o n g d e -

p e n d e n c e o n b o t h t h e a i r m a s s a n d t i m e o f d a y , a t -

t a i n in g i t s m i n i m u m v a l u e a t s o l ar n o o n a n d s t e a d i ly

i n c re a s e s a s w e m o v e a w a y f r o m s o l a r n o o n . O n e f a c to r

w h i c h m a y c o n t r i b u t e t o t h is i s t h a t d u r i n g m a n y c l e a r

d a y s t h e h u m i d i t y g e n e r a l l y a c h i e v e s i ts l o w e s t v a l u e

c l os e t o n o o n a n d i s u s u a l ly h i g h er i n t h e m o r n i n g a n d

a f t e r n o o n t h a n i t i s a t n o o n . T h e f i g u r e s a l s o d e a f l y

i n d i c a t e t h a t t h e e x t i n c t i o n c o e f f i c i e n t i s v e r y m u c h

a f fe c t e d b y t h e s e a s o n o f th e y e a r w i t h s u m m e r c o e f -

f i c ie n t s s u b s t a n t i a l l y h i g h e r t h a n t h e w i n t e r v a l u e s . T h i s

m a y b e e x p e c t e d f r o m o b s e r v i n g t h e w e a t h e r c o n d i t i o n s

i n A b u D h a b i d u r i n g s u m m e r a n d w i n t e r m o n t h s ;

w h e r e a s t h e v i s i b i li t y i s u s u a l l y h i g h a n d a t m o s p h e r i c

t u r b i d i t y l o w d u r i n g m o s t o f t h e t i m e i n w i n t e r , t h e

s u m m e r i s u s u a l l y c h a r a c t e r i z e d b y l o w v i s i b i l it y , h a z e ,

a n d t u r b i d a i r .

3 2 C O M P A R I S O N O F E X P E R I M E N T A L R E S U L T S

W I T H T H E O R Y

3 .1 T h e b e a m r a d i a ti o n c o m p o n e n t

T h e b e a m r a d i a t i o n i n c i d e n t o n a h o r i z o n t a l s u r fa c e

o n t h e g r o u n d w i ll n a t u r a l ly d e p e n d o n t h e a b s o r p t i o n

1 . 0 0

~ 0 . 8 0

c

M

0` 60

~ s

. ~ 0 ` t O

. _ c 0 . 2 0

0 . 0 0

t 2

3

m

a i r m a s s

4 5

Fig. 8. Var iat ion o f the extinct ion coef fic ient with air m ass

f or J anuar y and June ( 198 7) .

b e a m t r a n s m i t t a n c e

1

~b ~ ' . 4 . . . .

0

1 . 5 r n 5

a i r m a s s

Fig. 9. Var iat ion ofkb with air mass . Compar ison of the RSC

mo del with the exper imental data for January 1987, y = 4.0,

=

0.01.

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1 5 m 5

air mass

Solar radiation characterist ics in Ab u Dha bi 53

beam t i t t a n e e p r e s s u r e o f w a t e r v a p o r , p , , a s : y = 0 . 2 5 p , w i t h p , h a v -

i n g t h e u n i t o f m b a r . o i s / ~ n g s t r o m ' s t u r b i d i t y c o e f f i -

c i e n t w h i c h , a c c o r d i n g t o r e f. 4 , r a n g e s b e t w e e n 0 . 0 1

a n d 0 . 3 .

F r o m e q n ( 1 0 ) w e c a n w r i t e t h e b e a m f r a c t i o n i n

t e r m s o f th e d i f f e r e n t t r a s m i t t a n c e s

Fig. 10. Variation of kb with air mass. Comparison of the

RSC m odel with the experimental d ata for June 1987, y

= 10.0, o = 0.01.

a n d s c a t te r i n g a c t iv i t ie s ta k i n g p l a c e i n t h e a t m o s p h e r e .

T h e g e n e r a l f o r m o f t h e c l e a r s k y b e a m r a d i a t i o n m a y

b e e x p r e s s e d a s [ 4 ] :

( 1 0 )

b =

Go*

T a * T w T r T m

w h e r e

Go

i s t he ex t r a t e r r e s t r i a l r ad i a t i on on a h o r i zon t a l

su r face , 7 a , rw, r r , and zm a re , r e sp ec t i ve ly , t he t r ans-

m i t t a n c e d u e t o a b s o r p t i o n b y a t m o s p h e r i c g a se s , b y

w a t e r v a p o r , b y R a l e i g h s c a t t e r i n g a n d b y M i e s c a t te r -

i n g . E a c h o f th e s e f o u r t r a n s m i t t a n c e s r e p r e s e n t a s e p -

a r a t e a t t e n u a t i n g m e c h a n i s m a c t in g o n t h e i n c o m i n g

b e a m r a d i a t i o n .

B a s e d o n t h e t e x t s b y R o b i n s o n [ 5 ] a n d S e l l e r [ 6 ] ,

C a r r o l l [ 4 ] p r e s e n t e d r e l a t i o n s h i p s f o r t h e s e f o u r t r a n s -

m i t t a n c e s w r i t t e n i n t e r m s o f t h e p r e c i p i t a b l e w a t e r i n

t h e a t m o s p h e r e , t h e a t m o s p h e r i c t u r b i d i t y co e f f i ci e n t

a n d t h e a i r m a s s :

r a ( m ) = 1 0 - ( 0 0 0 2 m ) ( 1 1 )

r w ( m , y ) = 10 -[('4y''+O'Oty)ml

( 1 2 )

rr( m ) = 10 -(O'054m-O'OO88m2+l'OS lO-3m3-5 l lO-' m' ) ( 1 3 )

r m ( m , o ) = 10 -(0 666 m) (1 4 )

w h e r e y ( i n c m ) i s t h e p r e c i p i t a b l e w a t e r i n t h e a t -

m o s p h e r e a n d m a y b e e s t i m a t e d in t e r m s o f t h e p a r t i al

k b ( m , y , a ) = r a ( m ) ' r w ( m , y )

r r ( m ) ' r m ( m , t r ) ( 1 5 )

F i g u r e s 9 a n d 1 0 s h o w t h e m e a s u r e d a n d c a l c u l a t e d

v a l u es o f

kb

v e r s u s m f o r J a n u a r y a n d J u n e 1 98 7, r e -

s p e c t i v e ly , a n d i n d i c a t e a r e a s o n a b l e a g r e e m e n t b e -

t w e e n t h e R S C m o d e l a n d t h e a c t u a l d a t a . T h e b e a m

t r a n s m i t t a n c e i s s h o w n t o r e a c h i t s h i g h e s t v a l u e a t

n o o n a n d d r o p s d o w n o n e i th e r si d e o f n o o n t i m e t o

r e a c h i t s l o w e s t v a l u e j u s t a f t e r s u n r i s e o r j u s t b e f o r e

s u n s e t . W h i l e t h e t r e n d i s i d e n t i c a l f o r J a n u a r y a n d

J u n e , t h e b e a m f r a ct i o n s d u r i n g J u n e i s l o w e r t h a n

t h a t f o r J a n u a r y . T h e d i f f e r e n t v a l u e s o f y u s e d f o r

J a n u a r y a n d J u n e r e f le c t s t h e d i f f e re n c e in t h e a v e r a g e

h u m i d i t y p r e v a i li n g d u r i n g t h e s e m o n t h s i n A b u

D h a b i .

3 .2

T h e d i f f u s e r a d ia t i o n c o m p o n e n t

T h e d i ff u s e t r a n s m i t t a n c e kd c a n n o w b e d e t e r m i n e d

a s a f u n c t i o n o f t h e b e a m t r a n s m i t t a n c e k b . F o l lo w i n g

H o l l a n d s [ 7 ] a n d S u e h r c k e a n d M c C o r m i c k [ 8 ] , w e

a s s u m e t h a t t h e a t m o s p h e r e m a y b e d i v i d e d i n t o tw o

l a y e rs . T h e t o p l a y e r r e p r e s e n t s a l a y e r w i t h z e r o s c a t -

t e r i n g a n d c o m b i n e s t h e s e l e c t i v e a b s o r p t i o n b y a t -

m o s p h e r i c g a s e s s u c h a s H 2 0 a n d 0 3 , w h o s e a b s o r p t i o n

s h o w s o n l y a w e e k d e p e n d e n c e o n t h e a i r m a s s. H e n c e ,

t h e b e a m r a d i a t i o n t r a n s m i t t e d b y t h e t o p l a y e r a n d

i n c i d e n t o n t h e b o t t o m l a y e r i s ruGo, w h e r e r u i s t h e

t r a n s m i t t a n c e o f t h e u p p e r l a y er . T h e b o t t o m l a y er ,

w h i c h i s t h e l a y e r o f t h e m a i n c o n c e r n , i s a s s u m e d t o

e x h i b i t b o t h a b s o r p t i o n a n d s c a t te r i n g . T o s p e c i fy t h e

e x t e n t o f s c a t te r i n g r e l a t i v e t o a b s o r p t i o n , a s c a t t e r i n g

a lbed o , ~0, ha s b een de f ine d a s : o~ = f l s / ( f l , + f l a ) , wh e re

B~ a n d ~ a a r e t h e s c a t t e r i n g a n d a b s o r p t i o n c o e f f ic i e n ts

f o r b e a m r a d i a t i o n i n t h e b o t t o m l a ye r .

0 1

~ 0.2

. . -- ~ e

JanuQry 1987

7 0 7 , * o k o ,

1.0 2.0 3.0 &.O S.O

o i r m o s s

m

Fig. 11. The diffuse transm ittance vs. the air mass for Janu ary 1987, Bs = 0.8fie.

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54

A .M. EL-N A SH A R

di f fuse transmlt tanoe

k c l

0.8

0 . 2

0 . 1

J

/

/ _ _ _ - - - - - - - - - - - - -

air me l t s m

0ata -- kd

- O . f i ~ u - k b )

Fig. 12. The diffuse transmittance vs. air mass for

June 1987.

make a good fit of the experimental data for January

was estimated to be 0.8Be. Furthermore, the forward

and backward scattering fractions, J~ and J~, were

taken as 0.7 and 0.3, respectively.

Perhaps the simplest model for predicting the diffuse

transmittance for the two-layer atmosphere is that

based on the scattering of the lower layer being assumed

to be isotropic, imply ing that 50 of the scattered ra-

diati on would be scattered up and 50 scattered down

and eventually reaching the ground. Based on this

simplification, the diffuse energy reaching the grou nd

would be

k d = 0.5(ru -- k b ) . (19)

An equati on analogous to eqn ( 4) may be written to

express the beam radiation at a distance x measured

from the top edge of the lower atmospheric layer,

G o ( x ) = Gor,exp( -~dnx) (16)

where Be = BQ +/5~. The beam radiation scattered in

an infinitesimal layer of thickness dx around x may

be expressed as: dGs = G o ( x ) . B ~ . m . d x . Follow-

ing[ 8], we assume that o ut of the am oun t dG, scattered

in dx, an amount d G d reaches the ground which may

be writ ten as: d G d = d G ~ . r ( x ) , where r(x) is a ratio

given in [8] as:

J ) ~ ( x ) i

r x ) = ( 1 7 )

f f r x ) f + fbr x)o

whereJ]is the effective fraction scattered forward, and

J~ is the fraction scattered backward, r fa nd rb are the

transmittances of the scattered radiation to the ground

and to the top of the scattering layer, respectively. These

transmittances were approximated by that of beam ra-

diation thus,

-rf= exp[ -/3 e(L - X)]

and

rb = exp(-B~x)

The terrestrial diffuse radiation was obtained by

Suehrcke and McCormick[8] by integrating the

expression for

d G a

from x = 0 to x = L after substi-

tuting for dG, and r( x), thus

G a = G o Tu | L f f r f d x (18)

f~ I + fb~o

o

The diffuse transmittance, k d = G d / G o , was calculated

for different values of air mass and for each mo nth of

the year using the above equatio n, and the calculated Y

results were compared with values obtained from G r e e k

measured diffuse radiat ion in Abu Dhabi. Typical re- t~e

suits for Jan uar y 1987 are shown in Fig. 11. In this Bo

figure the scattering coefficient/3s which was found to Os

Using the empirical relationship between k0 and rn (eqn

( 15 )), the above expression for k d was plotted in Fig.

12. It can be seen that, in spite of its simplicity, this

model does predict the diffuse tran smit tance quite well.

4. CONCLUSION

Based on instanta neous measurements taken during

1987 for the global and diffuse rad iation in Abu Dhabi,

the clearness index, diffuse fraction, atmospheric

trans mitt ance, and the exti nction coefficient were cor-

related against the air mass and month of the year.

The diffuse fraction was also found to depend on both

the clearness index as well as the a ir mass with minimal

seasonal effects. The beam transmi ttance was estimated

theoretically using the two-layer atmosphere model and

the correlation for the extinction coefficient obtained

previously. This model was found to agree reasonably

well with the experimental data. The diffuse transm it-

tance was estimated using both the RSC model as well

as the isotropic scattering model; the results from both

these models were compared with the measured data.

The agreement appeared good.

d, b , c

d

h

A

Gb

o

G~

k,

ks

k~

L

m

P

P~

r( x )

N O MEN CLA TU RE

constants for a particular month

diffuse fraction

fraction of radiation scattered forward

fraction of radiation scattered backward

instantaneous beam radiation on a horizontal surface

instantaneous extraterrestrial radiation on a horizon-

tal surface

instantaneousdiffuse radiation on a horizontal surface

clearness index

beam transmittance

diffuse transmittance

height of bottom atmospheric layer

air mass

atmospheric transmittance

partial pressure of water vapor in the air

ratio of scattered radiation at x reaching ground

distance measured vertically downward from the top

edge of the bottom atmospheric layer

amount of precipitable water vapor in the air

extinction coefficient

extinction coefficientdue to absorption

extinction coefficient due to scattering

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So l a r r a d i a t i on c ha r a c t e r i s ti c s i n Abu Dh a b i

55

r u t r a n s m i t t a n c e d u e t o u p p e r a t m o s p h e r i c l a y e r

r = t r a ns m i t t a nc e due t o a bs o r p t i on by a tmos p he r i c ga se s

rw t r a n s m i t t a n c e d u e t o a b s o r p t i o n b y w a t e r v a p o r

T , t r a n s mi t t a nc e due t o Ra l e i gh s c a t t e r i ng

r ,~ t r a ns m i t t a nc e due t o Mi e s c a t t e r i ng

Ty

t r a n s m i t t a n c e o f f o r w a r d s c a tt e r ed r a d i a t i o n

r b t r a n s m i t t a n c e o f b a c k w a r d s c a t t er e d r a d ia t i o n

s c a t t e r i ng a l be do

Acknow ledgmen t s - -The a u t ho r w i s he s t o e xp r e ss h i s g r a t i tude

f o r t h e h e l p p r o v id e d b y M r . A m e r A . Q a m h e y a w h o c o m p i l ed

t h e d a t a a n d d e v e l o p e d t h e c o m p u t e r p r o g r a m w h i c h w a s u s ed

f o r d a t a a n a l y si s . T h e m o r a l s u p p o r t a n d e n c o u r a g e m e n t o f

t h e D i r e c t o r G e n e r a l , P o w e r a n d D e s a l i n a t io n P l a n t s o f t h e

W E D , A b u D h a b i i s v e ry m u c h a p p r e ci a te d .

R E F E R E N E S

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da i l y t o t a l s ho r t - wa ve r a d i a t i on on ve r t i c a l a nd i nc l i ne d

s u r f ac e s f r om s u ns h i ne r e c o r ds f o r l a ti t ude s 40 N t o 40 S .

I n : Proc. U.N. Conf. on N ew Sources o f Energy New York

Iiol. 4

p p . 3 79 . U n i t e d N a t i o n s, N e w Y o r k ( 1 9 6 4 ) .

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t r i bu t i on o f i n s t a n t a ne ous i n s o l a t ion va lue s, Solar Energy

4 0 ( 5 ) , 4 2 3 - 4 3 0 ( 1 9 8 8 ) .